Finite Group Databasebeta

← #25107997

Subgroups — #25107997

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143809C211yesmaximal, characteristic
2#19143292C211yesmaximal, characteristic, complemented
3#408×D43C211yesmaximal, characteristic, complemented
4#19135482C211yesmaximal, characteristic, complemented
5#19135302C211yesmaximal, characteristic, complemented
6#19135299C211yesmaximal, characteristic, complemented
7#19135246C211yesmaximal, characteristic, complemented
8#19135242C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134920C211yesmaximal, characteristic, complemented
11#19134894C211yesmaximal, characteristic, complemented
12#19134798C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C43×#1974C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063332C2211yescharacteristic, complemented
19C2×M16×D43C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583406C2211yescharacteristic
22#14583060C411yescharacteristic, complemented
23#14583058C411yescharacteristic, complemented
24#14583053C411yescharacteristic, complemented
25#14583048C411yescharacteristic, complemented
26#14583043C411yescharacteristic, complemented
27#14583041C411yescharacteristic, complemented
28#14583036C411yescharacteristic, complemented
29#14583031C411yescharacteristic, complemented
30#14582973—21no—
31#14582973—21no—
32(C22⋊D43)⋊C8—21no—
33(C22⋊D43)⋊C8—21no—
34C2×#13063260C2211yescharacteristic, complemented
35#14582925C2211yescharacteristic, complemented
36C2×#13063253C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic, complemented
39C2×#13063251C2211yescharacteristic
40#14582896C2211yescharacteristic
41#14582895C2211yescharacteristic
42#14582867C2211yescharacteristic
43#14582866C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582864—21no—
46#14582864—21no—
47#14582862C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C22⋊C8×D43—21no—
50C22⋊C8×D43—21no—
51#14582857C2211yescharacteristic, complemented
52C2×C8×Dic43C2211yescharacteristic, complemented
53C4×(C2×D43)⋊C4C2211yescharacteristic
54#14582664C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56#14582660C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582654C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C2×#135×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic, complemented
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic, complemented
64C43×#408C2211yescharacteristic
65C43×#408C2211yescharacteristic, complemented
66C2×C4×C8×C43C2211yescharacteristic, complemented
67C2×#10621902C2×C411yescharacteristic
68C2×#10621898—21no—
69C2×#10621898C2311yescharacteristic
70C2×#10621900—21no—
71C2×#10621900C2×C411yescharacteristic
72#41×D43—41no—
73#41×D43—41no—
74#41×D43—41no—
75#41×D43—41no—
76C2×Q8×D43C2×C411yescharacteristic
77C2×D4×D43—21no—
78C2×D4×D43C2×C411yescharacteristic
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81#13063345—41no—
82#13063345—41no—
83C2×#10621885C2×C411yescharacteristic
84C2×#10621883C2×C411yescharacteristic
85C2×#10621884C2×C411yescharacteristic
86C2×#10621882C2×C411yescharacteristic
87#13063332—41no—
88#13063332—41no—
89C2×#10621877—21no—
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621872—21no—
93M16×D43—41no—
94M16×D43—41no—
95C22×C43⋊C8—21no—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—21no—
99C2×C8×D43—41no—
100C2×C8×D43—41no—
101C2×C8×D43D411yescharacteristic
102C2×C8×D43D411yescharacteristic
103C2×C8×D43D411yescharacteristic
104C2×C8×D43D411yescharacteristic
105#13063306—21no—
106#13063301C2×C411yescharacteristic
107#13063301C2×C411yescharacteristic
108#13063296C2×C411yescharacteristic
109#13063296C2×C411yescharacteristic
110#13063293—21no—
111C4×C22⋊D43—21no—
112C4×C22⋊D43—21no—
113#13063284C2311yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×C4×Dic43C2311yescharacteristic
116#13063260—41no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063253—41no—
120#13063252—41no—
121#13063252—41no—
122#13063251—41no—
123#13063250C2×C411yescharacteristic
124#13063250C2×C411yescharacteristic
125#13063249C2×C411yescharacteristic
126#13063249C2×C411yescharacteristic
127#13063247C2×C411yescharacteristic
128#13063247C2×C411yescharacteristic
129#13063246C2×C411yescharacteristic
130#13063246C2×C411yescharacteristic
131C22⋊(C43⋊C8)—21no—
132C22⋊(C43⋊C8)—21no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139(C2×D43)⋊C8C2×C411yescharacteristic
140(C2×D43)⋊C8C2×C411yescharacteristic
141(C2×D43)⋊C8C2×C411yescharacteristic
142(C2×D43)⋊C8C2×C411yescharacteristic
143#13063235—21no—
144C8×Dic43—21no—
145C8×Dic43—41no—
146C43⋊#95—21no—
147C2×#41×C43C2311yescharacteristic
148C2×#41×C43C2311yescharacteristic
149#135×C43—41no—
150#135×C43—41no—
151C2×Q16×C43C2×C411yescharacteristic
152C2×SD16×C43C2×C411yescharacteristic
153C2×SD16×C43C2×C411yescharacteristic
154C2×D8×C43C2×C411yescharacteristic
155C2×M16×C43C2311yescharacteristic
156C2×M16×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C22×C8×C43C2311yescharacteristic
159C2×C42×C43C2311yescharacteristic
160#108×C43—41no—
161#104×C43—41no—
162#104×C43—41no—
163C22⋊C8×C43—21no—
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C4×C8×C43—41no—
168C23×D43—21no—
169C23×D43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178C2×Q8×C43C22×C411yescharacteristic
179C2×Q8×C43C22×C411yescharacteristic
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43#4111yescharacteristic
196#10621902—41no—
197#10621902—41no—
198Q8×D43—41no—
199Q8×D43—41no—
200#10621900—41no—
201#10621900—41no—
202#10621900—42no—
203#10621900—42no—
204D4×D43—42no—
205D4×D43—42no—
206D4×D43—41no—
207D4×D43—41no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—42no—
213#10621898—42no—
214C2×D172—21no—
215C2×D172C22×C411yescharacteristic
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—42no—
224C2×C4×D43—42no—
225C2×C4×D43C22×C411yescharacteristic
226C2×C4×D43C22×C411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×Dic86—21no—
230C2×Dic86C22×C411yescharacteristic
231Q16×C43—41no—
232SD16×C43—41no—
233SD16×C43—41no—
234D8×C43—41no—
235M16×C43—21no—
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43C22×C411yescharacteristic
246C2×C8×C43C22×C411yescharacteristic
247C2×C8×C43C2×D411yescharacteristic
248C2×C8×C43C2×D411yescharacteristic
249C42×C43—21no—
250C42×C43—21no—
251C22⋊Dic43—21no—
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254#10621885—41no—
255#10621884—41no—
256#10621883—41no—
257#10621882—41no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261C4⋊Dic43C22×C411yescharacteristic
262C4⋊Dic43C22×C411yescharacteristic
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265C4×Dic43—21no—
266C4×Dic43—21no—
267C4×Dic43—21no—
268#10621877—21no—
269#10621877—21no—
270#10621877—21no—
271#10621877—21no—
272#10621877—42no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—42no—
280C2×C43⋊C8C22×C411yescharacteristic
281C2×C43⋊C8C22×C411yescharacteristic
282C2×C43⋊C8C2×D411yescharacteristic
283C2×C43⋊C8C2×D411yescharacteristic
284#10621872—42no—
285C8×D43—41no—
286C8×D43—41no—
287C8×D43—41no—
288C8×D43—41no—
289C8×D43—42no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43C2×#4111yescharacteristic
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—22no—
296C22×D43—21no—
297C22×D43—41no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43C4×D411yescharacteristic
302C22×D43C4×D411yescharacteristic
303Q8×C43—21no—
304Q8×C43—21no—
305Q8×C43—21no—
306Q8×C43—21no—
307D4×C43—21no—
308D4×C43—21no—
309D4×C43—21no—
310D4×C43—21no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—41no—
334C22⋊D43—41no—
335C22⋊D43—42no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—22no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—42no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43C4×D411yescharacteristic
346C2×Dic43C4×D411yescharacteristic
347D172—21no—
348D172—21no—
349D172—42no—
350C4×D43—21no—
351C4×D43—21no—
352C4×D43—21no—
353C4×D43—21no—
354C4×D43—21no—
355C4×D43—21no—
356C4×D43—21no—
357C4×D43—21no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—41no—
361C4×D43—41no—
362Dic86—21no—
363Dic86—21no—
364Dic86—42no—
365C8×C43—21no—
366C8×C43—21no—
367C8×C43—21no—
368C8×C43—21no—
369C8×C43—41no—
370C8×C43—41no—
371C43⋊C8—21no—
372C43⋊C8—21no—
373C43⋊C8—21no—
374C43⋊C8—21no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377#22060—431nomaximal, Sylow
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43C2×C4×D411yescharacteristic
387C22×C43#53811yescharacteristic
388C22×C43#53811yescharacteristic
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—21no—
392C2×D43—21no—
393C2×D43—21no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—84no—
400C2×D43#44312yes—
401C4×C43—42no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43#51811yescharacteristic
405C4×C43#51811yescharacteristic
406C4×C43#53411yescharacteristic
407C4×C43#53511yescharacteristic
408Dic43—21no—
409Dic43—21no—
410Dic43—42no—
411Dic43—41no—
412Dic43—41no—
413Dic43—41no—
414#3002—431no—
415#2929—431no—
416C2×#408—431no—
417#1974—431no—
418#1974D4311yescharacteristic, complemented
419#1937—431no—
420#1937—431no—
421#1929—431no—
422#1929—431no—
423#1876—431no—
424#1876—431no—
425#1871—431no—
426#1855—431no—
427#1789—431no—
428C8×C22⋊C4—431no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—81no—
432C2×C43—81no—
433C2×C43#232111yescharacteristic
434C2×C43C2×#44311yescharacteristic
435C2×C43#295511yescharacteristic
436D43—22no—
437D43—41no—
438D43—81no—
439C22×#41—431no—
440C2×#135—431no—
441C2×#135C2×D4311yescharacteristic
442C2×#131—431no—
443C22×M16—431no—
444C23×C8—431no—
445#525—431no—
446#452—431no—
447#452—431no—
448#451—431no—
449#450—431no—
450#449—431no—
451#449—431no—
452#448—431no—
453#447—431no—
454#435—861no—
455#435—861no—
456C8×D4—861no—
457C8×D4—861no—
458C2×#108—431no—
459C2×#108C2×D4311yescharacteristic, complemented
460#424—431no—
461C2×#104—431no—
462C2×#104—431no—
463C2×#104—431no—
464C2×#104—431no—
465C2×#104C2×D4311yescharacteristic
466C2×#104C2×D4311yescharacteristic, complemented
467#416—431no—
468#416—431no—
469#408—431no—
470#408—431no—
471#408—431no—
472#408—861no—
473#408—861no—
474#408C2×D4311yescharacteristic
475#408C2×D4311yescharacteristic, complemented
476#407—431no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—861no—
479C2×C22⋊C8—861no—
480#405—431no—
481C2×C4×C8—431no—
482C2×C4×C8C2×D4311yescharacteristic, complemented
483C4×C22⋊C4—431no—
484#341—431no—
485#341—431no—
486#339—431no—
487#339—431no—
488#336—431no—
489#336—431no—
490C43#2206011yescharacteristic, complemented, Sylow
491C2×#41—431no—
492C2×#41—431no—
493C2×#41—431no—
494C2×#41—861no—
495C2×#41—861no—
496C2×#41—1721no—
497C2×#41—1721no—
498C2×#41—1721no—
499C2×#41—1721no—
500C2×#41C22×D4311yescharacteristic
501C2×#41C22×D4311yescharacteristic
502C22×Q8—431no—
503C22×D4—431no—
504C22×D4—861no—
505C23×C4—431no—
506C23×C4—861no—
507#135—41no—
508#135—41no—
509#135—1721no—
510#135—1721no—
511C2×Q16—431no—
512C2×Q16C4×D4311yescharacteristic
513C2×SD16—431no—
514C2×SD16—431no—
515C2×SD16C4×D4311yescharacteristic
516C2×SD16C4×D4311yescharacteristic
517C2×D8—431no—
518C2×D8C4×D4311yescharacteristic
519#131—1721no—
520#131—1721no—
521C2×M16—431no—
522C2×M16—431no—
523C2×M16—861no—
524C2×M16—861no—
525C2×M16—1721no—
526C2×M16—1721no—
527C2×M16C22×D4311yescharacteristic
528C2×M16C22×D4311yescharacteristic
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—431no—
533C22×C8—431no—
534C22×C8—431no—
535C22×C8—861no—
536C22×C8—861no—
537C22×C8—1721no—
538C22×C8—1721no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#123—861no—
542C22⋊Q8—431no—
543C22⋊Q8—431no—
544#121—431no—
545#121—431no—
546#120—861no—
547C4×D4—861no—
548C4×D4—861no—
549#117—431no—
550C2×C22⋊C4—861no—
551C2×C42—431no—
552C2×C42C22×D4311yescharacteristic
553#108—41no—
554#108—1721no—
555C4⋊C8—861no—
556C4⋊C8—861no—
557#104—41no—
558#104—41no—
559#104—1721no—
560#104—1721no—
561#104—1721no—
562#104—1721no—
563#103—431no—
564#103—431no—
565#103—431no—
566#103—431no—
567#102—431no—
568#102—431no—
569#102—431no—
570#102—431no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—431no—
576C22⋊C8—431no—
577C22⋊C8—431no—
578C22⋊C8—431no—
579C22⋊C8—861no—
580C22⋊C8—861no—
581C22⋊C8—861no—
582C22⋊C8—861no—
583C22⋊C8—861no—
584C22⋊C8—861no—
585C22⋊C8—861no—
586C22⋊C8—861no—
587#97—861no—
588C4×C8—41no—
589C4×C8—861no—
590C4×C8—1721no—
591#95—861no—
592C24—431no—
593C24—861no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—861no—
603#41—861no—
604#41—861no—
605#41—861no—
606#41—1722no—
607#41—1722no—
608#41—1721no—
609#41—1721no—
610#41—1722no—
611#41—1722no—
612#41—1721no—
613#41—1721no—
614C2×Q8—431no—
615C2×Q8—861no—
616C2×Q8—1721no—
617C2×Q8—1721no—
618C2×Q8C2×C4×D4311yescharacteristic
619C2×Q8C2×C4×D4311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—431no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—1721no—
630C2×D4—1721no—
631C2×D4—1722no—
632C2×D4—1722no—
633C2×D4C2×C4×D4311yescharacteristic
634C2×D4C2×C4×D4311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—1722no—
653C22×C4—1722no—
654C22×C4C23×D4311yescharacteristic
655Q16—41no—
656Q16—1721no—
657SD16—41no—
658SD16—41no—
659SD16—1721no—
660SD16—1721no—
661D8—41no—
662D8—1721no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—861no—
668M16—861no—
669M16—861no—
670M16—861no—
671M16—1722no—
672M16—1722no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—431no—
680C2×C8—431no—
681C2×C8—431no—
682C2×C8—431no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—1721no—
690C2×C8—1721no—
691C2×C8—1721no—
692C2×C8—1721no—
693C2×C8—1722no—
694C2×C8—1722no—
695C2×C8C2×C4×D4311yescharacteristic
696C2×C8C2×C4×D4311yescharacteristic
697C2×C8D4×D4311yescharacteristic
698C2×C8D4×D4311yescharacteristic
699C4⋊C4—431no—
700C4⋊C4—431no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C22⋊C4—861no—
704C22⋊C4—861no—
705C22⋊C4—864no—
706C22⋊C4—861no—
707C22⋊C4—861no—
708C22⋊C4—861no—
709C42—21no—
710C42—21no—
711C42—861no—
712C42—861no—
713C42—861no—
714C23—21no—
715C23—21no—
716C23—431no—
717C23—431no—
718C23—862no—
719C23—861no—
720C23—861no—
721C23—861no—
722C23—1721no—
723C23—1722no—
724C23—1722no—
725C23—1722no—
726C23#41×D4311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—861no—
732Q8—861no—
733Q8—1722no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—861no—
743D4—861no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1722no—
748D4—1722no—
749D4—1721no—
750D4—1721no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—431no—
761C2×C4—431no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—862no—
773C2×C4—861no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—1722no—
777C2×C4—1722no—
778C2×C4—1722no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4C22×C4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4#1306337011yescharacteristic
786C2×C4#1306337011yescharacteristic
787C2×C4#1306337011yescharacteristic
788C2×C4#1306337111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—861no—
796C8—861no—
797C8—861no—
798C8—861no—
799C8—1721no—
800C8—1721no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—432no—
810C22—861no—
811C22—861no—
812C22—861no—
813C22—861no—
814C22—861no—
815C22—3444no—
816C22—1722no—
817C22—1722no—
818C22—1721no—
819C22—1721no—
820C22—1721no—
821C22C4×D4×D4311yescharacteristic
822C22#1458348111yescharacteristic
823C22#1458348311yescharacteristic
824C4—42no—
825C4—41no—
826C4—41no—
827C4—861no—
828C4—861no—
829C4—1722no—
830C4—1721no—
831C4—1721no—
832C4—1721no—
833C4#1458337111yescharacteristic
834C4#1458337211yescharacteristic
835C4#1458345711yescharacteristic
836C4#1458346211yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—862no—
842C2—3441no—
843C2—1721no—
844C2#1913725411yescharacteristic
845C2#443×D4311yescharacteristic
846C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1974C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenter#1974D43
hypocenterC43#22060
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143292C2semidirect
3. #408×D43C2semidirect
4. #19135482C2semidirect
5. #19135302C2semidirect
6. #19135299C2semidirect
7. #19135246C2semidirect
8. #19135242C2semidirect
9. #19134924C2semidirect
10. #19134920C2semidirect
11. #19134894C2semidirect
12. #19134798C2semidirect
13. #19134537C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C43×#1974C2semidirect
18. C2×#13063332C22semidirect
22. #14583060C4semidirect
23. #14583058C4semidirect
24. #14583053C4semidirect
25. #14583048C4semidirect
26. #14583043C4semidirect
27. #14583041C4semidirect
28. #14583036C4semidirect
29. #14583031C4semidirect
34. C2×#13063260C22semidirect
35. #14582925C22semidirect
38. C2×#13063252C22semidirect
51. #14582857C22semidirect
52. C2×C8×Dic43C22semidirect
54. #14582664C22semidirect
55. #14582663C22semidirect
56. #14582660C22semidirect
57. #14582659C22semidirect
58. #14582654C22semidirect
59. #14582653C22semidirect
61. C2×#108×C43C22semidirect
63. C2×#104×C43C22semidirect
65. C43×#408C22semidirect
66. C2×C4×C8×C43C22semidirect
418. #1974D43semidirect
459. C2×#108C2×D43semidirect
466. C2×#104C2×D43semidirect
475. #408C2×D43semidirect
482. C2×C4×C8C2×D43semidirect
490. C43#22060semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191438092
#191432922
#408×D432
#191354822
#191353022
#191352992
#191352462
#191352422
#191349242
#191349202
#191348942
#191347982
#191345372
C8×(C2×D43)⋊C42
C43×#19742
#2206043